AMUCHMA-NEWSLETTER-23

Chairman: Paulus Gerdes (Mozambique)

Secretary: Ahmed Djebbar (Algeria)

Treasurer: Salimata Doumbia (Côte d'Ivoire)

Members: Kgomotso Garegae-Garekwe (Botswana), Maassouma Kazim
(Egypt), Cornelio Abungu (Kenya), Ahmedou Haouba (Mauritania),
Mohamed Aballagh (Morocco), Ruben Ayeni (Nigeria), Abdoulaye Kane
(Senegal), David Mosimege (South Africa), Mohamed Souissi (Tunisia),
David Mtwetwa (Zimbabwe)

TABLE OF CONTENTS

2. Meetings, exhibitions, events

5. Theses

6. Sources

7. Reprints

8. Have you read? (#286-#296) --- 2nd web page

9. Announcements --- 2nd web page

10. Addresses of scholars and institutions mentioned in this newsletter --- 2nd web page

11. New recipients--- 2nd web page

Do you want to receive the next AMUCHMA-Newsletter

Universidade Pedagógica (UP), Maputo (Mozambique), 06.25.1999

2. MEETINGS, EXHIBITIONS, EVENTS

**2.1 CIMPA School on the History of Mathematics** (cf. AMUCHMA
21:7).

The International Center for Pure and Applied Mathematics (CIMPA)
organised, in collaboration with Unesco-Egypt, from January 23
to February 3, 1999 in Mansurah (Egypt) a school on the **History
of Mathematics in the Mediterrenean from Antiquity to the 18th
century**. Claude Lobry and Roshdi Rashed coordinated the school.
There were fifty-four participants (21 Egyptians, 12 Lebanese,
4 Moroccans, 2 Algerians, 2 Tunisians, 8 French, 2 Italians, 2
Indians, 1 Thai). The lectures were given at the faculty of Sciences
of the El-Mansurah University. The following themes were presented:

* R. Rashed: *From Diophantus to Fermat*;

* C. Houzel, *From Euler to Gauss*;

* P. Crozet: *Plane geometry and the theory of conic sections*;

* R. Morelon: *Mathematical astronomy from Hipparchus to Copernicus*;

* H. Bellosta: *Infinitesimal geometry*;

* E. Giusti: *Western mathematics from the Renaissance to modern
times*;

* M. Zerner: *Tangent problems from Newton to Leibniz*;

* J. Delattre: *Neopythagorican arithmetic*;

* F. Vofea: *History of Egyptian mathematics*;

* M. Benmiled: *Book X of Euclid's Elements*;

* R.K. Bhattacharyy: *History of Indian mathematics*;

* N. Farès: *The limits of Arab algebra: Sharaf al-Dîn
al-Tûsî*.

**2.2 European Summer School on the History of
Mathematics (Belgium)**

The Faculty of Mathematics of the University of La Laguna (Tenerife,
Canary Islands) organised an interdisciplinar seminar entitled
"*Mathematics and Culture: New Tendencies in Ethnomathematics
and the History of Mathematics*" (5 to 7 October 1999).
The following themes were presented:

* Paulus Gerdes (Mozambique): *Ethnomathematics: Origins, development
and some tendencies*;

* Paulus Gerdes: *Examples of mathematical ideas south of the
Sahara*;

* José Barrios García (Canary Islands): *Mathematical
ideas of the Guanches of Tenerife*.

On October 7, Paulus Gerdes delivered at the same Faculty the
inaugural lecture of the 1999-2000 academic year, entitled "*On
geometry south of the Sahara*".

**2.4 Workshop on Mathematics and Mathematics
Education in Africa**

Mohamed El Tom (Sudan), chairman of the African Mathematical
Union Commission on Mathematics Education (AMUCME) and visiting
professor at Teachers College, Columbia University (New York,
USA), organised on the weekends of November 6 and 7 and November
13 and 14, 1999, a workshop on mathematics and mathematics education
in Africa. The following talks were related to the history of
mathematics education in Africa:

* Eric Karuhije (Uganda): *Mathematics education in Uganda in
historical perspective*;

* Paulus Gerdes (Mozambique): *Mathematics and mathematics education
in Mozambique in historical perspective*;

* Bruce Vogeli (USA): *US involvement in African Mathematics
education development*.

**2.5 National Colloquium on Teaching Mathematics
in the University (Algeria)**

Professor Rachid Bebbouchi of the Mathematics Department of
the Houari Boumediene University of Algiers (Algeria), organised
from November 27 to 30, 1999, a National Colloquium on the Teaching
of Mathematics in Algeria. Several papers were presented related
to the history of mathematics:

* Ahmed Djebbar: *Role of the history of mathematics in the
teaching of mathematics*;

* Youcef Guergour: *Some themes from the history of geometry
for use in teaching*;

* Youcef Atik: *The method of exhaustion in the Arab mathematical
tradition*;

* Kaddour Guerbati: *Mathematics and poetry: yesterday and today*.

**2.6 Papers presented at recent meetings**

* At the International Study days on Number (Peyresc, France,
7-10 September 1999), Ahmed Djebbar (Algeria) presented a paper
on "*From the thought number to the idea of number: some
aspects of arithmetic praxis and its continuation in Andalusia
and the Maghreb*".

* On October 11, 1999, Paulus Gerdes (Mozambique) gave a lecture
on "*Culture and Mathematics in Africa*" at the
Centre for African and Development Studies of the Higher Institute
for Economy and Management of the Technical University of Lisbon
(Portugal).

* At the Colloquium held in Marrakech (Morocco, 14-16 October
1999) on Ibn Tufyal, a philosopher from the 12th century who lived
in Marrakech, Ahmed Djebbar (Algeria) presented a paper on "*Mathematical
and astronomical activities in Andalusia and in the Maghreb during
the time of Ibn Tufayl*".

* The first theme "*Arabic Mathematics and its influence
on European science*" of the seminar on "Galilei
and the beginnings of modern science" was presented by Ahmed
Djebbar (Algeria) on October 25, 1999, at the University of La
Laguna and on October 26 at the University of Las Palmas (Canary
Islands). The seminar is organised by the 'Fundación Canaria
Orotava de Historia de la Ciencia'.

* At the First Ethnomathematics Congress of Bolivia (Santa Cruz de la Sierra, Bolivia, 27-30 October 1999), Paulus Gerdes spoke about the development of mathematics education and ethnomathematics in Mozambique. The Congress was coordinated by Oscar Pacheco Rios, Chairman of the Bolivian Ethnomathematics Study Group.

* On November 16, 1999, Paulus Gerdes (Mozambique) conducted
at Rutgers University (New Brunswick NJ, USA) a seminar on "*Mathematical
aspects of the weaving of the 'milala' dance bell in northern
Mozambique*".

* At the National Colloquium on Non-Linear Analysis, organised
by professor M. S. Moulay at the Houari Boumediène University
(22-24 November, 1999, Algiers, Algeria), Ahmed Djebbar gave the
opening address entitled "*Mathematical paradigms during
the history of the elaboration of the concept of real number*".

* On November 25, 1999, Ahmed Djebbar (Algeria) gave a public
address on "*Scientific activities in the Maghreb during
the Ottoman epoch*" at the occasion of the celebrations
of the millennial of the foundation of the city of Algiers (Algeria).

* On December 11, 1999, Ahmed Djebbar (Algeria) presented the
paper "*Contribution of Arab mathematicians to algebra*"
at the Franco-Italian Colloquium on "Italian algebraists"
(Lille, France).

* On December 17, 1999, Ahmed Djebbar (Algeria) presented the
paper "*Montucla's treatment of the history of Arab mathematics
and astronomy*" at the Colloquium organised at the occasion
of the bicentenary of the death of Montucla, the first great French
historian of mathematics (Lyon, France).

3. CURRENT RESEARCH
INTERESTS

* Abdelmalek Bouzari is preparing a doctoral thesis ('thèse d'état') at the University of Annaba (Algeria) on "The conic sections in the Kitab al-istikmal of al-Mu'taman (11th century): Contribution to the study of the history of geometry in Andalusia and in the Maghreb".

This section is reserved for questions that readers would like to have answered; these are the 'queries'. The answers will be the 'notes'. If you have questions or answers about sources, dates, names, titles, facts, or other such matters related to the history of mathematics in Africa, frame them in clear and concise language and send them to the editors. If you are answering a question, make clear reference to that question. All readers may send both questions and answers. Each will be published with the name of the sender.

Professor David Singmaster (UK) sent us the following query:

* "There is a puzzle, often called Solomon's Seal, which has a small board with three holes. The loop of a string is passed through the center hole and the two ends are passed through the loop. A ring is placed on each of the strings and then each end is passed through an end hole and tied. It looks like two oops hanging off the board with a ring on each loop. The object is to get the two rings onto one of the loops. In 1975, Fred Grunfeld's Games of the World, p. 267, calls this 'an African puzzle'. Since then, this has been repeated in other books. However, I can find no source or evidence for this assertion. Perhaps Grunfeld first came across the puzzle in Africa. In European literature, the puzzle is depicted and described as far back as 1636 in Germany, 1725 in France and 1747 in Italy. Do you know anything about this or similar topological puzzles in Africa? Indeed, anything about African puzzles would interest me."

The Solomon's Seal described is equivalent to the 'pèn'
puzzle from West Africa (Guinean forest). I describe it (and some
other topological puzzles) in my paper "On mathematics in
the history of Sub-Saharan Africa" (*Historia Mathematica*,
New York, Vol. 21, 1994, 345-376). Several references are indicated.
My source on the 'gèn' game was the book by C. Beart: "*Jeux
et jouets de l'Ouest Africain*", IFAN, Dakar, 1955, p.
413 (PG).

Dr. Michael Morelli (USA) sent us the following query:

* 'What do you know about math books in the 14th century university
library of Timbuktu that was uncovered by Henry Louis Gates of
Harvard University?"

* In June 1999, **Abdelmalek Bouzari** defended at the E.N.S.
of Algiers (Algeria) a 'Magister' thesis, entitled "*The
conic sections in the Arab mathematical tradition through a treatise
attributed to al-Khazin (10th century)*".

The thesis contains a historical presentation of the conic sections
in the Greek and Arab traditions, a critical edition on
the basis of two existing manuscripts of a text from the
10th century, attributed to the mathematician al-Khazin, and a
mathematical analysis of the contents of this text.

* Also in June 1999, **Khadidja Kouidri** defended at the
E.N.S. of Algiers (Algeria) a 'Magister' thesis, entitled "*The
method of false position in the Arab mathematical tradition*".

This thesis contains an analysis of a certain number of Arab texts
produced between the 10th and the 14th century, which deal with
the solution of linear equations and of systems of linear equations
by means of the methods of false position.

**6.1 Further sources on numeration in Africa **(Cf. AMUCHMA 22:4, 6-10)

(Paulus Gerdes)

Ludwig Gerhardt, **Zahlensysteme in der nigrianischen Plateausprachen
Import und Export in Naira und Schilling **[Numeral systems
in Nigerian Plateau languages Import and export in Naira
and Shilling], manuscript, Würzburg (Germany), 1985

(see English language version, 1987).

Ludwig Gerhardt, **Some remarks on the numerical systems of
Plateau languages**, *Afrika und Übersee*, 70 (1987),
19-29

Discusses the transition from duodecimal to decimal numeration
in some languages belonging to the eastern Kainju group (like
Eggon) and some Western and central Plateau languages (Nigeria).

Hubert Grimme, **Nachtrag zu A. Klingenhebens Studie über
die Berberischen Zählenmethoden** [Comments on A. Klingenheben's
study of the Berber methods of counting], *Zeitschrift für
Eingeborenensprachen*, 17 (1926/27), 230-234

Complements Klingenheben's paper with further information on the
vigesimal numeration.

Carl Hoffmann, **Zur Verbreitung der Zahlwortstämme in
Bantu-sprachen** [On the distribution of number word roots in
Bantu languages], *Afrika und Übersee*, 37:2 (1952/3),
65-80

Discusses the distribution of the roots for the number words 1
to 10. For the number words 2 to 5 and 10 the uniformity is greater
than for the number words for 1, and 6 to 9 (p. 78).

August Klingenheben, **Zu den Zählenmethoden in den Berbersprachen
**[On the counting methods in the Berber methods], *Zeitschrift
für Eingeborenen-sprachen*, 17 (1926/27), 40-51

Analyses different numeration systems in Berber languages in north-west
Africa: mostly decimal, sometimes quinar-trigesimal (Nefusa language),
sometimes vigesimal (Sus region [Morocco]) and the interaction
with Arabic.

Theodor Kluge, **Die Zahlbegriffe der Sudansprachen, ein Beitrag
zur Geistesgeschichte der Menschen** [The number concepts in
the Sudanese languages, a contribution to the spiritual history
of man], edition of the author, Berlin-Steglitz, 1937, 260 pp.,
17 maps

Presents the number words in 976 Sudanese languages and dialects,
organised in 16 regional groups from the Senegal-Guinea to the
Nile-Chad. A comparative analysis of the languages in each group
is included. The sources (mostly grammars and dictionaries) used
by the author are indicated.

Theodor Kluge, **Die Zahlbegriffe der Australier, Papua und
Bantuneger nebst einer Einleitung über die Zahl; ein Beitrag
zur Geistesgeschichte des Menschen** [The number concepts of
the Australian, the Papua and the Bantu Negroes together with
an introduction to number; a contribution to the spiritual history
of man], edition of the author, Berlin-Steglitz, 1938, 304 pp.,
6 maps

The section on Bantu languages presents first the number words
in 274 Bantu languages (and dialects), organised by geographical
region (197-276), followed by a comparative analysis of the number
word root and structure (277-300). The sources used by the author
are not indicated.

G. Lindblom, **The magic significance of numbers**, in:
*The Akamba in British East Africa*, 1908, 306-310

"... Odd numbers are generally considered disastrous or at
least unlucky ..." A contrary state of affairs is encountered
"at a medicine man's divination, as the pebbles that fall
out of his calabash are a good omen if they are odd and vice versa..."
(p. 306).

Carl Meinhof, **Rezension von M. Schmidl 'Zahl und Zählen
in Afrika'**, *Zeitschrift für Kolonialsprachen*,
6 (1915-1916), 251-252

Review of #49.

Carl Meinhof, **Rezension von K. Sethe 'Von Zahlen und Zahlworten
bei den alten Ägyptern und was für andere Völker
und Sprachen daraus zu lernen ist'**, *Zeitschrift für
Kolonialsprachen*, 8 (1917-1918), 268-270

Review of the book by K. Sethe. The author is criticised for the
fact that he advances with a comparison with Semitic languages,
but forgets to study the relationship with African languages.

K. Sethe**, Von Zahlen und Zahlworten bei den alten Ägyptern
und was für andere Völker und Sprachen daraus zu lernen
ist. Ein Beitrag zur Geschichte von Rechenkunst und Sprache **[On
numbers and numerals among the ancient Egyptians and what can
be learned from them concerning other peoples. A contribution
to the history of arithmetic and language], Trübner, Straßburg,
1916, 147 pp.

Bairu Tafla, **Some remarks on numerical idioms recurring
in Ethiopian history**, *Afrika und Übersee*, 70 (1987),
73-98

" certain numbers [e.g. 2, 4, 40, 44, 80, 7] in the Semitic
languages of Ethiopia form components of idiomatic expressions
in which they lose their accurate mathematical significance and
assume figurative meanings, or connotations which have no relation
whatsoever to their original meaning. Some imply greatness, wholeness
or totality; others indicate excessiveness of amount, or fantastical
size" (p. 92.

Anton Vorbichler, **Zahlensysteme des Balese-Obi und des Mamwu
(Mangbetu-Efe-Gruppe der zentralsudanesischen Sprachen **[Number
systems of the Balese-Obi and Mamwu (Mangbetu-Efe-Group of the
central African languages)], *Afrika und Übersee*, 1983,
Vol. 66, 131-140

Comparative study of numeration in the Balesi-Obi (decimal) and
Mamwu languages spoken in Northeastern Congo / Zaire, based on
data collected in the period 1954-1960. In the Mamwu language
exist basic number words for 1, 2, 3, 4, 5, and 10, and by using
also the terms 'elí' (hand), 'qarú' (foot) and 'múdo'
(human, 20), the cardinals are formed.

(to be continued)

**6.2 Further sources on String Figures in Africa
**(Cf. AMUCHMA 9; #175, 193, 214, 223, 228; AMUCHMA 21:7)

Recent issues of the *String Figure Magazine* contains
the following information related to the African continent:

* Border between two countries, collected by E. D. Earthy from
the Thonga people of Mozambique, Africa [Vol. 3(4), December 1998,
11-14], based on information contained in the book *Valenga
Women*, Oxford University Press, London, 1953, 95-101, written
by E.D. Earthy;

* The eagle and its nest, collected by Hugh Tracey from the Mashona
people of Southern Zimbabwe [Vol. 4(1), March 1999, 11-15], based
on the paper "**String Figures (***madandi ) found
in Southern Rhodesia*",

* A bed, collected by William Cunnington at the south end of Lake Tanganyika [Vol. 4(3), September 1999, 16-18], based on information contained in the paper "

The *Bulletin of the International String Figure Association*
includes the paper:

* Carey C.K. Smith: **String Figures from the Congo** (1997,
Vol. 4, 135-184). "The article presents sixty-seven string
figures gathered at Upoto in the former Belgian Congo by Mrs.
Ethel M. Smith during the years 1910-1914. Among her informants
were members of the Lingombe, Lifoto, Ngombe, Ngwenzali, and Ngwengali
tribes. Unlike F. Starr's Congo collection published in 1909,
the Smith collection includes methods of construction for each
figure. In an appendix to this article, the author presents methods
for making thirty-nine of the sixty-two figures described by Starr."
The Starr's collection may be found in the following paper:

* F. Starr:** Ethnographic notes from the Congo Free State**,
*Proceedings of Davenport Academy of Sciences*, 1909, vol.
12, 148-175

The book "**Fascinating String Figures**" (Dover,
New York, 1999) contains a compilation of articles from the String
Figure Magazine. It includes two figures from Africa: "A
hammock" (Zanzibar, Tanzania) and "Two eyes" (Liberia).

The web-page of the International String Figure Association (ISFA)
is:

http://www.isfa.org

The Institute for the History of Arabic-Islamic Science at the Johann Wolfgang Goethe University (Frankfurt am Main, Germany) collected and started the reprinting of a series of papers and books on "Islamic mathematics and science". Related to the history of mathematics in Africa are the following reprints:

**Volumes 14-15**: *Codex Leidensis 399,1. Euclidis Elementa
ex interpretatione ***al-Hadschdschadschii cum commentariis
**al-Narizii

**Volume 16**: *The Commentary of ***Pappus on
Book X of Euclid's Elements. Arabic text and translation by William
**Thomson

**Volume 17**: ** Euclid in the Arabic Tradition.
Texts and Studies. Collected and reprinted**. I. Edited by Fuat
Sezgin in collaboration with M. Amawi, C. Ehrig-Eggert, and E.
Neubauer. 1997, 340 pp.

This volume contains the following papers:

* Franz Woepcke: Sur les traductions arabes de deux ouvrages
perdus d'Euclide (1-31);

* Ludwig Oftendinger: Beiträge zur Wiederherstellung der
Schrift des Euklides über die Theilung der Figuren (33-52);

* Moritz Steinschneider: Die "mittleren" Bücher
der Araber und ihre Bearbeiter (54-96);

* Moritz Steinschneider: Euklid bei den Arabern. Eine bibliographische
Studie (97-126);

* Moritz Steinschneider: Simplicius, der Mathematiker (127-128);

* Maximilian Curtze: Das angebliche Werk des Euklides über
Waage (129-130);

* Maximilian Curtze: Zwei Beiträge zur Geschichte der Physik
im Mittelalter. I. Das Buch Euklids de gravi et levi (131-134);

* Hermann Weissenborn: Die Übersetyung des Euklid aus dem
Arabischen in das Lateinische durch Adelhard von Bath nach zwei
Handschriften der Kgl. Bibliothek in Erfuhrt (135-160);

* Antonio Favaro: Notizie storico-critiche sulla Divisione delle
aree (161-186);

* Johnan L. Heiberg: Die Nachrichten der Araber (187-209);

* Johnan L. Heiberg: Die arabische Tradition der Elemente Euklid's
(211-231);

* Johnan L. Heiberg: Beiträge zur Geschichte der Mathematik
im Mittelalter. I. Liber Archimenidis de comparatione figuraram
circularium ad rectilineas. II. Euklid's Elemente im Mittelalter
(233-264);

* Johnan L. Heiberg: Paralipomena zu Euklid II (266-271);

* Martin Klamroth: Über den arabischen Euklid (272-328).

**Volume 18**: ** Euclid in the Arabic Tradition.
Texts and Studies. Collected and Reprinted**. II. Edited by
Fuat Sezgin in collaboration with M. Amawi, C. Ehrig-Eggert, and
E. Neubauer. 1997, 324 pp.

This volume contains the following papers:

* Rasmus O. Besthorn: Über den Commentar des Simplicius
zu den Elements (1-2);

* Heinrich Suter: Einiges aus Nassir ed-Dins Euklidausgabe (3-6);

* Heinrich Suter: Review of: *Codex Leidensis 399* (8-18);

* Heinrich Suter: Zur Frage des von Nairiyi zitierten Mathematikers
"Diachasimus";

* Heinrich Suter: Über den Kommentar des Muhammed ben 'Abdelbâgî
zum zehnten Buche des Euklides (20-37);

* Heinrich Suter: Der Kommentar des Pappus zum X. Buch des Euklides
aus der arabischen Übersetyung des Abû 'Othman al-Dimashki
ins Deutsche übertragen (39-110);

* Mansion: Sur le commentaire dßAnaritius relatif aux Éléments
d'Euclide (111-113);

* Karl Lokotsch: Avicenna als Mathematiker, besonders die planimetrischen
Bücher seiner Euklidübersetzung (115-141);

* Razmond Archibald: Euclid's Book on Divisions of Figures with
a restoration based on Woepcke's text and on the *Practica geometricae*
of Leonardo Pisa (143-236);

* Giuseppe Furlani: Bruchstücke einer syrischen Paraphrase
der "Elemente" des Euklides (237-287);

* Eilhard Wiedemann: Zu der Redaktion von Euklids Elementen durch
Nasir al Dîn al Tûsî (288-296);

* Gotthelf Bergsträßer: Pappos' Kommentar zum Zehnten
Buch von Euklid's Elementen. Beiträge zu Text und Übersetzung
(297-324).

**Volume 19**: ** Euclid in the Arabic Tradition.
Texts and Studies. Collected and reprinted**. III. Edited by
Fuat Sezgin in collaboration with M. Amawi, C. Ehrig-Eggert, and
E. Neubauer. 1997, 310 pp.

This volume contains the following papers:

* David Smith: Euclid, Omar Khayyam, and Saccheri (1-6);

* Albert G. Kapp: Arabische Übersetzer und Kommentatoren
Euklid's, sowie deren math.-naturwiss. Werke auf Grund des Ta'rikh
al-Hukama des Ibn al-Qifti (8-121);

* M.-A Kugener: Les versions latines des "Éléments"
d'Euclide conservées à la bibliothèque publique
de Bruges (122-124);

* Claire Baudoux: La version syriaque des "Éléments"
d'Euclide (125-127);

* Claire Baudoux: Une édition polyglotte orientale des
"Éléments" d'Euclide : La version arabe
d'Ishâq et ses dérivées (128-129);

* Gustav Junge: Das Fragment der lateinischen Übersetzung
des Pappus-Kommentars zum 10. Buche Euklids (131-147);

* Clemens Thaer: Die Euklid-Überlieferung durch Al-Tûsî
(148-153);

* Clemens Thaer: Euklids Data in arabischer Fassung (155-163);

* A. S. Ünver: Avicenna's praise of Euclid (164-166);

* Edward B. Plooij: Euclid's conception of ratio and his definition
of proportional magnitudes as criticized by Arabian commentators
(167-243);

* Marshall Clagett: The medieval Latin translation from the Arabic
of the Elements of Euclid, with special emphasis on the versions
of Adelard of Bath (244-270);

* 'Abdalhamid Sabra: "Burhan" Nasiraddin al-Tusi 'ala
musadarat Uqlidis al-hamisa [The demonstration of Euclid's fifth
postulate by Nasiraddin al-Tusi] (272-309).

**Volume 23**: ** Abu Kamil Shuja' ibn Aslam (3rd/9th
cent.). Texts and Studies. Collected and reprinted**. III.
Edited by Fuat Sezgin in collaboration with M. Amawi, C. Ehrig-Eggert,
and E. Neubauer. 1997, 262 pp.

This volume contains the following papers:

* Gustavo Sacerdote: Il trattato del pentagono e del decagono
di Abu Kamil Shogia' ben Aslam ben Mohamed. Per la prima volta
publicato in italiano (1-26);

* Heinrich Suter: Die Abhandlung des Abu Kamil Shoga' b. Aslam
"über das Fünfeck und das Zehneck" (27-54);

* Heinrich Suter: Das Buch der Seltenheiten der Rechenkunst von
Abu Kamil el-Misri. Übersetzt und mit Kommentar versehen
(56-76);

* Louis Karpinski: The algebra of Abu Kamil Shoka' ben Aslam (78-93);

* Louis Karpinski: The algebra of Abu Kamil (95-106);

* Josef Weinberg: Die Algebra des Abu Kamil Soga' ben Aslam (107-251).

(to be continued)

**8. **Have you read?**
- 2nd web page**

**9. **Announcements**
- 2nd web page**

**10. **Addresses
of scholars and institutions mentioned in this newsletter**
- 2nd web page**

**11. **New
Recipients** - 2nd web page**

Thanks to Scott Williams, the English language
edition of all issues of the **AMUCHMA Newsletter** is also
accessible on the following website: **http://www.math.buffalo.edu/mad/AMU/amuchma_online.html**

Please note the address of the above website
changed to the present with AMUCHMA 21.

The English version of AMUCHMA
23 is reproduced and distributed

with financial support from **SIDA**-**SAREC** (Sweden)